Complex image compression

ABSTRACT

Complex image data is transformed to a holographic representation of the image. A subset of the holographic representation is modeled. Model parameters constitute a compressed image representation. A two-dimensional Fourier transform can be applied to obtain the holographic image. Modeling includes applying an analysis portion of an adaptive analysis/synthesis linear prediction methodology to a subset of the holographic representation to obtain an autoregressive model. Prior to modeling, one-dimensional Fourier transform can be performed on the holographic representation and the linear prediction is one-dimensional. Model parameters are preferably quantized. Embodiments include determining error between the model and the model&#39;s input data. There the compressed image representation the error, which also can be quantized. The subset of the holographic representation can be less than all the representation. The subset can be a plurality of complete rows; preferably substantially symmetric about 0 Hz.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Embodiments of the invention disclosed herein may have been conceived or first actually reduced to practice in the performance of work under a classified contract with the Unites States Air Force. As a result, the Government may have certain rights in those inventions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to application Ser. No. 11/267,177 filed Nov. 7, 2005. This application is also related to application Ser. No. 11/898,763 filed Sep. 14, 2007 entitled Magnitude Image Compression.

FIELD OF THE INVENTION

Embodiments of the invention disclosed herein relate to data compression. More specifically, some embodiments relate to compression of image data.

BACKGROUND OF THE INVENTION

Most image compression algorithms, either lossy or lossless, have focused on the real-valued pixel intensities of the image. As a basis for compression, most of the techniques attempt to exploit local correlations among data elements, e.g., pixel intensities. For example, many lossless compression algorithms for imagery seek to capture the local correlation among pixel intensities using very low order pre-determined linear filters. The error residual output of the filters are then encoded and transmitted to the receiver. Longer prediction filters are not helpful for compressing image pixel intensity data since the correlations are localized.

The transform coding used in JPEG is the most popular approach for lossy image compression. It also tries to capture the local correlations in image intensities by dividing the figure into small 8×8 blocks of data. These localized blocks are transformed using a two-dimensional Discrete Cosine Transform (DCT) and the largest transform coefficients are retained and encoded for transmission. JPEG 2000 is a recent image compression standard based on a wavelet approach that uses sub-banding to decompose the image into low-pass and high-pass regions. The outputs of the filter banks are down-sampled, quantized, and encoded. The decoder decodes the coded representations, up-samples and reconstructs the signal using a synthesis filter bank. In JPEG 2000 the filter banks are predetermined and are independent of the source data. The information necessary to reconstruct the image comes from transmitting selected outputs of the analysis filters. These methods have been useful for compressing electro-optical (EO) imagery; but have not focused on phase preserving compression such as the present invention.

BRIEF SUMMARY OF THE INVENTION

The invention includes methods, systems, and computer program products for image compression. Various embodiments of the invention include steps, modules and subsystems for performing the following activities. Pixel intensity data of an image is transformed to a holographic representation of the image. For a complex image, the image is transformed to a holographic representation to facilitate modeling the data. A subset of the holographic representation is modeled, and the model parameters and prediction residual constitute a compressed representation of the image.

In some embodiments, a two-dimensional Fourier transform is applied to obtain the holographic image. Modeling includes applying an analysis portion of an adaptive analysis/synthesis prediction methodology to a subset of the holographic representation. Applying the modeling to a subset of the holographic representation enables a resolution/compression trade-off. Linear prediction is preferred as the adaptive analysis/synthesis prediction methodology. In some embodiments, prior to modeling, a one-dimensional Fourier transform is performed on the holographic representation and the linear prediction is one-dimensional. In some embodiments the image data is symmetrically extended to ensure real-valued model parameters and prediction residuals. In some embodiments, particularly for complex images, the data is not symmetrically extended resulting in complex model parameters and prediction residuals.

In some embodiments model parameters are quantized. Some embodiments include determining an error residual between the model and the input data to the model. In those embodiments, the compressed representation of the image includes the residual, which is also quantized.

Other embodiments of the invention include methods, systems, and computer program products for communicating images. In addition to the activities described above, these embodiments involve communicating the model parameters to a destination. At the destination a holographic representation is synthesized from the model. The synthesized holographic representation is transformed to a set of pixel intensity data of the image. In some embodiments, the destination and source are co-located. In some embodiments, the synthesized holographic representation is created using the error as an excitation source. In still further embodiments, the decompression steps are performed at a destination other than the computer platform where compression is performed.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Other objects, features, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiment and certain modifications thereof when taken together with the accompanying drawings in which:

FIG. 1 a illustrates an original image and an image reconstructed after being compressed in accordance with embodiments of the invention.

FIG. 1 b illustrates the phase preservation property of embodiments of the invention.

FIG. 1 c illustrates an original image and an image reconstructed after being compressed in accordance with embodiments of the invention.

FIG. 2 illustrates methods of the invention.

FIG. 3 illustrates a relationship between a holographic representation (analogous to a radar phase history) of image data and a viewable image.

FIG. 4 illustrates methods of the invention as applied to Synthetic Aperture Radar data.

DETAILED DESCRIPTION OF THE INVENTION

As required, detailed embodiments of the present invention are disclosed herein. However, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms. The figures are not necessarily to scale, and some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention.

Embodiments of the present invention employ adaptive analysis/synthesis techniques typically used for compression of speech data. Such compression techniques generally achieve very high compression ratios if there is a valid parametric model of the data source, since the techniques typically require that only the model parameters be transmitted for reconstruction of the original data. Although successful for speech compression, adaptive analysis/synthesis techniques have not been successfully employed before for image compression. One reason that typical image compression techniques do not rely on an adaptive model-based analysis/synthesis architecture is because it is generally believed that while speech can be modeled as the output of a linear filter, most images cannot. Thus the absence of strong global correlations in the pixel intensities across an image discourages use of adaptive analysis/synthesis compression architectures that rely on the availability of stationary data to train a parametric model of the source.

Embodiments of the invention create a representation of imagery data that allows an image to be modeled using an adaptive analysis/synthesis compression architecture. Some embodiments of the invention first transform the image data (e.g., pixel intensities) into a representation that replaces local correlations in pixel intensities with global correlations in a wave format that remains mathematically stationary throughout the transformed data. This allows a useful formation of model parameters based on a relatively large collection of training data with substantially the same statistics. Additionally, stationarity allows the modeled image data to be synthesized (e.g., reconstructed at a destination) using only one set of model parameters that capture the stationary data statistics. Thus the data transformation to this globally-correlated representation enables an analysis/synthesis compression architecture for imagery.

The present disclosure refers to the transformed pixel intensity data as the image's “holographic representation” since it exhibits holographic properties in the sense that all regions of the transformed data contain the spatial frequencies present throughout the image—similar to the way an optical hologram contains all spatial frequencies present in the imaged object. Typically, the holographic representation is achieved by applying a two-dimensional Fourier Transform (2-D FT) to the pixel intensities of the image. This transforms pixel amplitudes into a complex 2-D plane wave whose frequencies in the horizontal and vertical directions corresponds to the horizontal and vertical positions of the pixel. Thus the 2-D FT transform uncovers a natural wave structure underlying the image. In this representation the data are statistically stationary since the localized pixel energy has now been spread across the entire data representation in the form of a 2-D plane wave. The pixel frequencies are plane waves adding constructively and destructively in the holographic representation. The presence of the complex wave forms at each point in the transformed domain means that the transformed data can be effectively modeled with adaptive linear filter techniques, such as Linear Predictive Coding (LPC). One particular LPC approach that can be utilized to model the transformed data is autoregressive (AR) modeling. The 2D plane waves can be de-correlated by applying a 1D FT and thereby enabling 1D modeling.

Once the transformed data have been modeled, the model parameters and prediction residual are quantized, encoded, and transmitted to a receiver (or stored locally) for future reconstruction and viewing. Compression is the result of the reduced model parameter size relative to the original complex image data and the dynamic range reduction of the prediction residual. The image is reconstructed by decoding the model parameters and synthesizing the holographic data in a manner similar to many of the ways that speech is synthesized in methods such as vocoding. The data synthesis is performed by passing the prediction residual through a filter loaded with the AR model parameters to regenerate an approximation of the de-correlated data. The reconstructed de-correlated data is transformed back to an estimate of the original image with a 1D FT. FIG. 1 a provides an example of an original image 110 and a reconstructed image 120 synthesized using only the AR prediction model parameters and the prediction residual. FIG. 1 b illustrates the phase-preserving property of the compression performance of FIG. 1 b. FIG. 1 c provides an additional example of an original image 130 and a reconstructed image 140 synthesized using only the AR prediction model parameters and the prediction residual.

The compression of an image may be further increased with only gradual degradation in the reconstructed image by taking advantage of another property of the holographic representation. Since the holographic domain is composed of the 2-D plane waves of the pixel values, the pixel values are represented in all portions of the holographic data. This means that only portions of the holographic data actually need to be modeled and encoded. The effect of selecting only a portion of the holographic data to model results in a lower resolution reconstructed image; however the image degradation is gradual when compared to the increase in compression.

Subsequent paragraphs provide detailed description of various embodiments of the invention. FIG. 2 provides an overview of the method illustrating, among other things:

-   -   transforming 220 original image data 210 into a holographic         representation amenable to modeling;     -   pre-processing the holographic representation in some cases,         e.g., select a portion of the holographic representation,         perform DFT on columns 230;     -   modeling the holographic representation or its preprocessed form         240;     -   quantizing the model parameters 250;     -   creating a synthesized holographic time series representation         from model parameters 270;     -   transforming 280 the synthesized holographic time series         representation into a reconstituted image 290; and     -   optionally making the above process lossless by determining an         error signal between a representation locally reconstituted from         the model and the original representation 252, quantizing the         error signal 254, and using it, to synthesize 256 the         holographic (or hybrid) representation to form a lossless image         of the original at the destination.

Embodiments of the invention have applicability to Synthetic Aperture Radar (SAR) data compression. SAR is a remote sensing technology that synthesizes an antenna aperture using the motion of a radar transmitter to yield high spatial resolution radar images. Referring to FIG. 3, in SAR technology the temporal wave nature of radar returns is represented by a phase history 310 (analogous to the holographic representation of the present invention). Note that SAR phase history is a holographic representation and therefore may be used interchangeably regarding the present invention. Applying a 2D Discrete Fourier Transform (DFT) 320 to the phase history forms a complex image.

Since the holographic representation of a SAR image is both mathematically stationary and largely composed of correlated exponentials, methods of the present invention can be used to advantage for compressing the image based on the phase history representation. FIG. 4 illustrates the combination of DFTs with analysis/synthesis modeling to implement a method of the invention.

First, a DFT is applied 410 to each column of the 2D phase history of an image. Applying a DFT de-correlates the 2D complex exponentials of the phase history into rows of 1D complex exponentials, eliminating the need to model 2D statistics. Note if all the rows are used, the de-correlated data can be obtained simply by a 1D DFT to the complex image data. In some embodiments, the data is transformed using the DFT and directly modeled.

The AR models for each row are formed using standard linear prediction 420, which is an effective technique for finding models of stationary correlated data sets. The modeler uses weighted linear combination of previous signal values to model the current value. Weight coefficients, w, are found using the normal equations that find the expected correlations between past and current values for stationary sources. A covariance matrix of these coefficients with Toeplitz symmetry is formed by zero padding. This symmetry allows a computationally efficient solution to w, e.g., using the popular Levinson-Durbin recursion. In other embodiments, adaptive analysis/synthesis approaches to modeling that are known to those skilled in the art may be used in place of Linear Prediction Coding. The coefficients are then quantized 430.

Since linear predictive coefficients are known to be sensitive to quantization effects, quantization in the present embodiments is preferably performed using alternate representations of the coefficients such as line spectral pairs (LSP) or reflection coefficients.

Given that there is a strong correlation between reflection parameters from row to row, trellis coded quantization (TCQ) is applied 430 to the difference between the LSP parameters of each row. TCQ uses a Viterbi algorithm to select the path, through a state machine, that causes the least amount of quantization distortion. The branches of the state machine refer to specific quantization levels. For illustration, four states can be used with two branches going in and out of each state, for a total of eight quantization levels. Other quantization methods know to those skilled in the art, e.g., uniform, scalar, vector, Huffman, arithmetic, vector codebook, quantization, split matrix, can be used in place of TCQ.

Quantized model parameters, ŵ, plus the quantized prediction residual represent a compressed representation of the original image. Among other things, this compressed representation can be stored for later retrieval within the system that compressed the image, written to removable memory for transfer to another location or archive, and transmitted over a communications medium to a receiver at a destination.

At the destination, or upon retrieval from a storage medium, the AR model weights are loaded into the synthesis portion of a prediction model used to analyze the weights in the first place. Row data Ŷ is synthesized by passing the quantized predication residual through the loaded prediction model 440.

A DFT then operates 450 on each reconstructed row to transform the data into the reconstituted complex image. The reconstituted complex image preserves the phase information from the original complex image. This aspect of the invention is important for applications that use the phase information. The magnitude of the complex image may be viewed and an observable slight loss in resolution can occur due to the sliding window snapshot process. Zero-padding and further transformation 490 can render the reconstituted image in a size corresponding to the original image. In this fashion, embodiments of the invention combine the efficiency of model-based compression with a vocoding reconstruction technique to achieve compression gain with phase preservation and acceptable loss in viewable image quality.

Not all of the holographic representation needs to be used in order to produce a model that will result in a good approximation of the original image. Since the dominant frequencies are found throughout the holographic representation, those can be captured in smaller segments (e.g., fewer rows or fewer columns) of the holographic representation. The synthesized holographic AR time series representation can be zero-padded so that the transform back to complex imagery is the same size as the original image. Thus the holographic representation can be used to further compress the image at a cost of decreased resolution. In preferred embodiments, the portion of the holographic representation chosen to be modeled is symmetric about 0 Hz.

As another alternative, Code Excited Linear Predication (CELP) can be used to approximate the error residual.

Embodiments of the invention also can applied to lossless compression. Lossless compression typically incorporates a data model, such as AR modeling described above, to reduce the estimated entropy of the signal. By transmitting both the model parameters and the error residual formed between the model's estimate and the original signal, the original image can be losslessly reconstructed. If the error residual has a lower dynamic range or entropy, a lossless compression gain is achieved. In general, the similarity between filter coefficients of adjacent rows should be utilized in the quantization method chosen.

While SAR applications (where a holographic representation of an image is typically available as its phase history) were presented as an illustrative embodiment, any set of pixel intensity data that can be 2-D transformed into a holographic representation can be modeled directly by methods such as 2-D Linear Prediction, Hidden Markov models, and other adaptive analysis/synthesis statistical modeling techniques known to those skilled in the art.

The above-described system can be implemented on a computing device, such as a personal computer, Personal Digital Assistant (PDA), interne enabled telephone, dedicated image compression/decompression device, or the like, or a separate programmed general purpose computer having an image management capabilities. Additionally, the systems and methods of this invention can be implemented on a special purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit element(s), and ASIC or other integrated circuit, a digital signal processor, a hard-wired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA, PAL, or the like. In general, any device capable of implementing a state machine that is in turn capable of implementing the processes described herein can be used to implement the systems and techniques according to this invention.

While the embodiments illustrated herein show the various components of the system co-located, it is to be appreciated that the various components of the system can be located at distant portions of a distributed network and/or the Internet, or within a dedicated secure, unsecured and/or encrypted system. Thus, it should be appreciated that the components of the system can be combined into one or more devices or co-located on a particular node of a distributed network, such as a telecommunications network. As will be appreciated from the following description, and for reasons of computational efficiency, the components of the system can be arranged at any location within a distributed network without affecting the operation of the system. Moreover, the components could be embedded in a dedicated image encoding and/or decoding machine.

Furthermore, it should be appreciated that the various links, including the channel, connecting the elements can be wired or wireless links, or any combination thereof, or any other known or later developed element(s) that is capable of supplying and/or communicating data to and from the connected elements. The term module as used herein can refer to any known or later developed hardware, software, firmware, or combination thereof that is capable of performing the functionality associated with that element. The terms determine, calculate and compute, and variations thereof, as used herein are used interchangeably and include any type of methodology, process, mathematical operation or technique.

Furthermore, the disclosed methods may readily be implemented in software using object or object-oriented software development environments that provide portable source code that can be used on a variety of computer or workstation platforms. Alternatively, the disclosed system may be implemented partially or fully in hardware using standard logic circuits or, for example, a VLSI design. Whether software or hardware is used to implement the systems in accordance with this invention is dependent on the speed and/or efficiency requirements of the system, particular function, and the particular software or hardware systems or microprocessor or microcomputer systems being utilized. The systems and methods illustrated herein can be readily implemented in hardware and/or software using any suitable systems or structures, devices and/or software, such as JAVA®, by those of ordinary skill in the applicable art from the functional description provided herein and with a basic general knowledge of the computer and data or image processing arts.

Moreover, the disclosed methods may be readily implemented in software, e.g., as a computer program product, executed on a programmed general purpose computer, a special purpose computer, a microprocessor, or the like. In these instances, the systems and methods of this invention can be implemented as a program embedded on a personal computer such as a JAVA®, CGI or Peri script, as a resource resigning on a server or graphics workstation, as a routine embedded in a dedicated image system, or the like. The systems and methods of this invention can also be implemented by physically incorporating this system and method into a software and/or hardware system, such as the hardware and software systems of a computer. Such computer program products and systems can be distributed and employ a client-server architecture. While exemplary embodiments disclosed herein use still imagery to enable principles of the invention, these principles can also be applied to, e.g., video, medical imagining, transmission of images to wireless devices. 

We claim:
 1. A computer implemented method of image processing, the method comprising: transforming, by the computer, complex data of an image to a holographic representation of the image, wherein said complex data includes phase information; modeling, by the computer, a subset of the holographic representation using autoregressive modeling to form a model having model parameters; determining, by the computer, a prediction residual between the model and input data to the model; whereby the model parameters and prediction residual constitute a compressed representation of the image; synthesizing, by the computer or a different computer, a holographic representation from the model and prediction residual; and transforming, by the computer or the different computer, the synthesized holographic representation to a set of complex data of the image, wherein the set of complex data of the image preserves the phase information of the complex data of the image.
 2. The method of claim 1 wherein transforming the complex data comprises applying, by the computer, a two-dimensional Fourier transform to obtain the holographic representation of the image; and modeling comprises one-dimensional modeling.
 3. The method of claim 1 wherein transforming the complex data comprises applying, by the computer, a two-dimensional transform to obtain the holographic representation of the image.
 4. The method of claim 3 further comprising, prior to modeling, performing, by the computer, a one-dimensional Fourier transform on the holographic representation; and wherein modeling comprises one-dimensional modeling.
 5. The method of claim 1 further comprising communicating the model parameters and prediction residual to the different computer.
 6. A non-transitory computer-readable medium for image processing comprising: a transform module transforming complex data of an image to a holographic representation of the image, wherein said complex data includes phase information; a modeling module modeling a subset of the holographic representation by applying autoregressive modeling to the subset of the holographic representation to form a model having model parameters, and determining a prediction residual between the model and the input data to the model, whereby the model parameters and prediction residual constitute a compressed representation of the image; and a synthesis module synthesizing a holographic time series representation from the model parameters and prediction residual, and transforming the synthesized holographic time series representation to a set of complex data of the image, wherein the set of complex data of the image preserves phase information of the complex data of the image.
 7. The non-transitory computer-readable medium of claim 6 wherein transforming complex data comprises applying a two-dimensional Fourier transform to obtain the holographic representation of the image; and modeling comprises one-dimensional modeling.
 8. The non-transitory computer-readable medium of claim 6 wherein transforming complex data comprises applying a two-dimensional transform to obtain the holographic representation of the image.
 9. The non-transitory computer-readable medium of claim 8 further comprising, prior to modeling, performing a one-dimensional Fourier transform on the holographic representation; and wherein modeling comprises one-dimensional modeling. 